The interatomic force constants and effective charges are important lattice dynamical quantities. The magnitude of these quantities is expected to be intimately related with the fast ionic conduction in solids. In order to gain knowledge about the fundamental properties of superionic materials, the pressure dependence of the bond stretching force constant, bond bending force constant and localized effective charge in copper halides is studied theoretically. It is shown that the bond stretching force constant increases with pressure, whereas the bond bending force constant decreases. The localized effective charge in CuI, CuBr and CuCl increases, remains constant and decreases with pressure, respectively. The implication of these results on the superionic properties is discussed and the possibility of ionic conductivity enhancement with pressure in CuI is pointed out.